A person pushes horizontally with constant force P on a 230 N box resting on a frictionless horizontal floor.

Which of the following statements about this box is correct?

A.The box will accelerate no matter how small P is.
B. The box will not accelerate unless P > 230 N.
C. The box will move with constant velocity because P is constant.
D.Once the box is set moving, it will come to rest after P is removed.

A. Because on a fricitionless horizontal surface any finite mass will accelerate if any finite net force is applied in any direction that is not perpendicular to the said surface.

Well, it's always important to remember that boxes have feelings too. So let's see what we can do to make this box move, shall we?

A. The box will accelerate no matter how small P is. Well, even the tiniest force can get the box rolling. It may be slow, but hey, we all have to start somewhere.

B. The box will not accelerate unless P > 230 N. Oh no, don't underestimate the power of a small push! Even a force less than 230 N can get this box moving.

C. The box will move with constant velocity because P is constant. Ah, if only life were that simple. Unfortunately, constant force doesn't necessarily mean constant velocity. The box may accelerate if there are no other opposing forces acting on it.

D. Once the box is set moving, it will come to rest after P is removed. Well, unless there's someone waiting to catch it, the box will keep on sliding until it encounters another force, like friction.

So, I'll go with option A. The box will accelerate no matter how small P is. Keep those pushes coming!

The correct statement about the box is:

B. The box will not accelerate unless P > 230 N.

Explanation:
According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration. In this case, the only force acting on the box is the horizontal force applied by the person.

If P is less than 230 N, the net force on the box will be less than its weight (230 N) and it will not be able to overcome the gravitational force pulling it downward. Therefore, the box will not accelerate.

If P is equal to 230 N, the net force on the box will be zero, and it will remain at rest or move with a constant velocity due to the absence of any unbalanced forces.

Only if P is greater than 230 N, the net force on the box will be greater than its weight, resulting in acceleration in the direction of the applied force.

To determine which statement is correct about the box, we need to apply Newton's Second Law of Motion. According to this law, the net force acting on an object is equal to the product of its mass and acceleration.

In this case, the box is resting on a frictionless horizontal floor, so there is no opposing force due to friction.

Statement A: "The box will accelerate no matter how small P is."
This statement is incorrect. Since the box is on a frictionless surface, the only force acting on it is the horizontal force P. If P is zero or too small, there will be no net force acting on the box, and it will not accelerate.

Statement B: "The box will not accelerate unless P > 230 N."
This statement is incorrect as well. The weight of the box is 230 N, but there is no requirement for P to be greater than 230 N for acceleration to occur. As long as the horizontal force P is non-zero, the box will experience a net force and will accelerate.

Statement C: "The box will move with constant velocity because P is constant."
This statement is also incorrect. If the force applied to the box is constant and non-zero, the box will continue to accelerate in the direction of the force. Its velocity will increase over time, not remain constant.

Statement D: "Once the box is set moving, it will come to rest after P is removed."
This statement is incorrect. In the absence of any opposing forces like friction, the box will continue to move with a constant velocity once it has been set in motion. Removing force P would only stop its further acceleration but would not cause it to come to a rest immediately.

Based on the explanations above, none of the statements are correct.